In a camp, there is a meal for $120$ men or $200$ children. If $150$ children have taken the meal, how many men will be catered to with the remaining meal?

### Concept & Unitary Method When a resource can support either quantity A or quantity B, we can establish an equivalence ratio to convert the remaining portion from one demographic to the other. ### Step-by-Step Solution * **Given**: Total meal = $120$ men OR $200$ children. * **Calculation**: Establish the equivalent ratio: $$ 120 \text{ men} = 200 \text{ children} $$ $$ 1 \text{ child} = \frac{120}{200} \text{ men} = \frac{3}{5} \text{ men} $$ The meal is designed for $200$ children, but $150$ children have already eaten. Remaining meal capacity = $200 - 150 = 50$ children. Convert the remaining capacity to men: $$ \text{Men} = 50 \times \frac{3}{5} = 30 \text{ men} $$ ### Exam Strategy & Shortcut Find the fraction of the meal remaining. $150$ out of $200$ children ate, meaning $75\%$ of the food is gone. $25\%$ of the food is left. $25\%$ of $120$ men is simply $\frac{120}{4} = 30$ men. ### Common Pitfall Trying to subtract children from men directly without applying the equivalency ratio. ### Final Answer Therefore, the correct answer is **30**.